Consider two firms engaging in sequential Stackelberg competition.
Suppose firm 1 decides its quantity x1 first and firms 2 follows after observing x1. The demand function of the market is
x( p ) = 100 - 0.1p and the cost function for both firms are c( x ) = FC + 5 x^2
(a) Suppose first that FC = 0. Derive firm 2's best response function to observing firm 1's output level x1.
(b) What output level will firm 1 choose?
(c) What output level does that imply firm 2 will choose?
(d) What is the equilibrium Stackelberg price?
(e) Now suppose FC is not zero. What is the lowest FC at which firm 1 does not have to engage in strategic entry deterrence in order to keep firm 2 out of the market?